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A neutral core of degressively proportional allocations under lexicographic preferences of agents

Author

Listed:
  • Katarzyna Cegiełka

    (Wroclaw University of Economics and Business)

  • Piotr Dniestrzański

    (Wroclaw University of Economics and Business)

  • Janusz Łyko

    (Wroclaw University of Economics and Business)

  • Arkadiusz Maciuk

    (Wroclaw University of Economics and Business)

  • Maciej Szczeciński

    (Wroclaw University of Economics and Business)

Abstract

One of the main problems of practical applications of degressively proportional allocations of goods and burdens is lack of uniqueness of this principle. Even under given boundary conditions of allocation, i.e. determined minimal and maximal amounts of a good that can be assigned in a given allocation, there are usually many feasible solutions. The lack of formal rules of allocation is the reason why the allocation is typically a result of negotiations among its agents. A number of allocations favor some of agents or their groups, therefore other agents cannot accept them. The aim of this paper is to indicate a way of reducing the set of all feasible solutions exclusively to those that are neutral to all agents. As a result of the term of lexicographic preference of allocation agents defined on the basis of the relation theory followed by a numerical analysis of sets of all feasible solutions, it is possible to determine a core of this set in the form of a subset of all feasible solutions that are acceptable by all agents. In addition, this subset can be further divided into smaller subsets with regard to the degree of acceptance of their elements. Theoretical analysis is complemented by case studies, one of which is application of this idea to the allocation of seats in the European Parliament among the member states of the European Union.

Suggested Citation

  • Katarzyna Cegiełka & Piotr Dniestrzański & Janusz Łyko & Arkadiusz Maciuk & Maciej Szczeciński, 2021. "A neutral core of degressively proportional allocations under lexicographic preferences of agents," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 11(4), pages 667-685, December.
    • Handle: RePEc:spr:eurase:v:11:y:2021:i:4:d:10.1007_s40822-021-00174-5
    DOI: 10.1007/s40822-021-00174-5
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    1. Claus Beisbart & Luc Bovens, 2007. "Welfarist evaluations of decision rules for boards of representatives," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 29(4), pages 581-608, December.
    2. Duff, Andrew, 2012. "Finding the balance of power in a post-national democracy," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 74-77.
    3. Yukio Koriyama & Jean-François Laslier & Antonin Macé & Rafael Treibich, 2013. "Optimal Apportionment," Journal of Political Economy, University of Chicago Press, vol. 121(3), pages 584-608.
    4. Salvador Barbera & Matthew O. Jackson, 2006. "On the Weights of Nations: Assigning Voting Weights in a Heterogeneous Union," Journal of Political Economy, University of Chicago Press, vol. 114(2), pages 317-339, April.
    5. Xu, Xiaozhan, 2001. "The SIR method: A superiority and inferiority ranking method for multiple criteria decision making," European Journal of Operational Research, Elsevier, vol. 131(3), pages 587-602, June.
    6. Nicholas Miller, 2012. "Why the Electoral College is good for political science (and public choice)," Public Choice, Springer, vol. 150(1), pages 1-25, January.
    7. Macé, Antonin & Treibich, Rafael, 2012. "Computing the optimal weights in a utilitarian model of apportionment," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 141-151.
    8. Grimmett, G.R. & Oelbermann, K.-F. & Pukelsheim, F., 2012. "A power-weighted variant of the EU27 Cambridge Compromise," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 136-140.
    9. Sascha Kurz & Nicola Maaser & Stefan Napel, 2017. "On the Democratic Weights of Nations," Journal of Political Economy, University of Chicago Press, vol. 125(5), pages 1599-1634.
    10. Bahadir Fatih Yildirim & Burcu Adiguzel Mercangoz, 2020. "Evaluating the logistics performance of OECD countries by using fuzzy AHP and ARAS-G," Eurasian Economic Review, Springer;Eurasia Business and Economics Society, vol. 10(1), pages 27-45, March.
    11. Jürgen Habermas, 2017. "Citizen and State Equality in a Supranational Political Community: Degressive Proportionality and the Pouvoir Constituant Mixte," Journal of Common Market Studies, Wiley Blackwell, vol. 55(2), pages 171-182, March.
    12. Moberg, Axel, 2012. "EP seats: The politics behind the math," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 78-84.
    13. Zhang, Tao & Zou, Heng-fu, 1998. "Fiscal decentralization, public spending, and economic growth in China," Journal of Public Economics, Elsevier, vol. 67(2), pages 221-240, February.
    14. Pham, Ngoc Anh, 2019. "Lorenz comparison between Increasing serial and Shapley value cost-sharing rules," Economics Letters, Elsevier, vol. 179(C), pages 49-52.
    15. Laslier, Jean-François, 2012. "Why not proportional?," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 90-93.
    16. Katarzyna Cegiełka & Janusz Łyko & Radosław Rudek, 2019. "Beyond the Cambridge Compromise algorithm towards degressively proportional allocations," Operational Research, Springer, vol. 19(2), pages 317-332, June.
    17. Grimmett, Geoffrey R., 2012. "European apportionment via the Cambridge Compromise," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 68-73.
    18. Florek, Jan, 2012. "A numerical method to determine a degressive proportional distribution of seats in the European Parliament," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 121-129.
    19. Pierre‐Richard Agénor & Kyriakos C. Neanidis, 2011. "The Allocation Of Public Expenditure And Economic Growth," Manchester School, University of Manchester, vol. 79(4), pages 899-931, July.
    20. Janusz Łyko & Radosław Rudek, 2017. "Operations research methods in political decisions: a case study on the European Parliament composition," Computational and Mathematical Organization Theory, Springer, vol. 23(4), pages 572-586, December.
    21. Słomczyński, Wojciech & Życzkowski, Karol, 2012. "Mathematical aspects of degressive proportionality," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 94-101.
    22. Ramírez González, V. & Martínez Aroza, J. & Márquez García, A., 2012. "Spline methods for degressive proportionality in the composition of the European Parliament," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 114-120.
    23. Serafini, Paolo, 2012. "Allocation of the EU Parliament seats via integer linear programming and revised quotas," Mathematical Social Sciences, Elsevier, vol. 63(2), pages 107-113.
    24. Janusz Łyko & Ewa Łyko, 2020. "The Composition of the European Parliament During the 2019–2024 Term in Light of Legal Provisions and the Rules of Fair Distribution," Eurasian Studies in Business and Economics, in: Mehmet Huseyin Bilgin & Hakan Danis & Ender Demir (ed.), Eurasian Economic Perspectives, pages 363-374, Springer.
    25. Jason Papathanasiou & Nikolaos Ploskas, 2018. "Multiple Criteria Decision Aid," Springer Optimization and Its Applications, Springer, number 978-3-319-91648-4, June.
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    Cited by:

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    More about this item

    Keywords

    Fair division; Lexicographic order; Degressive proportionality; European Parliament;
    All these keywords.

    JEL classification:

    • D30 - Microeconomics - - Distribution - - - General
    • D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement
    • D69 - Microeconomics - - Welfare Economics - - - Other

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